A function is an operation denoted by a function name followed by zero or more input values that are enclosed in parentheses. It represents a relationship between a set of input values and a set of result values. The input values to a function are called arguments.
An aggregate function receives a set of values for each argument (such as the values of a column) and returns a single-value result for the set of input values. Certain rules apply to all aggregate functions.
A scalar function can be used wherever an expression can be used. The restrictions on the use of aggregate functions do not apply to scalar functions, because a scalar function is applied to single set of parameter values rather than to sets of values. The argument of a scalar function can be a function. However, the restrictions that apply to the use of expressions and aggregate functions also apply when an expression or aggregate function is used within a scalar function.
For example, the argument of a scalar function can be a aggregate function only if a aggregate function is allowed in the context in which the scalar function is used.
A table function can be used only in the FROM clause of a statement. Table functions return columns of a table and resemble a table created through a CREATE TABLE statement. Table functions can be qualified with a schema name.
A row function can be used only in contexts that are specifically described for the function.
Note: A user defined function cannot be a Row function (Ref:IBM)